# Long Division Index

Long Division is easy, **once you get the idea**.

Hopefully some of these pages will "click" with you, and you will be a master!

See Why Long Division? below

## Understanding Long Division

## Long Division

## Practice

## Advanced

## Why Long Division

The simplest way to do division is by **repeated subtraction**:

### Example: What is 48 / 12?

- Start with 48, subtract 12, we get 36
- Repeat: 36-12 = 24
- Repeat: 24-12 = 12
- Repeat: 12-12 = 0

We did 4 subtractions, so 48 / 12 = 4

But this could take a long time for something like 3768 / 12

### Example: What is 3768 / 12?

- Start with 3768, subtract 12, we get 3756
- Repeat: 3756-12 = 3744
- Repeat: 3744-12 = 3732
- Repeat: 3732-12 = 3720
- ... oh No! This will take a long long time!

Maybe we could do 100 subtracts in one go:

- Start with 3768, subtract
**100 lots of 12**, we get 3768-1200 = 2568 - Repeat: 2568-1200 = 1368
- Repeat: 1368-1200 = 168

Now lets move to doing 10 subtracts in one go:

- 168, subtract
**10 lots of 12**, we get 168-120 = 48

Now lets move to singles:

- 48, subtract 12, we get 36
- Repeat: 36-12 = 24
- Repeat: 24-12 = 12
- Repeat: 12-12 = 0

So we did **3 lots of 100**, **1 lot of 10** and **4 single** subtracts of 12, which is a total of **314 subtracts of 12**

So 3768 / 12 = 314

That is the **Idea behind Long Division**

And we usually write it down like this:

12 )3768

0

37

36

16

12

48

48

0

It may look a little strange at first, but can you see the "3768" near the top?

And then the "12" at its left, and the actual answer of "314" at the top.

That shows us we worked out **3768 / 12 = 314**

- Now look down for the "36": That is where we tackled the
**100s**(3 × 12 = 36) - And a bit below that is the "12", which is where we did the
**10s**(1 × 12 = 12) - And at the bottom is the "48" (4 × 12 = 48)

So we tackled the 100s, then the 10s, then the units, just like before.

And the "0" at the end means that after all the subtracts there is nothing left over.

Continue on and learn how to do this yourself!